Question: Solve for $y$, $ \dfrac{2}{4y} = \dfrac{3}{8y} + \dfrac{2y + 10}{4y} $
Answer: First we need to find a common denominator for all the expressions. This means finding the least common multiple of $4y$ $8y$ and $4y$ The common denominator is $8y$ To get $8y$ in the denominator of the first term, multiply it by $\frac{2}{2}$ $ \dfrac{2}{4y} \times \dfrac{2}{2} = \dfrac{4}{8y} $ The denominator of the second term is already $8y$ , so we don't need to change it. To get $8y$ in the denominator of the third term, multiply it by $\frac{2}{2}$ $ \dfrac{2y + 10}{4y} \times \dfrac{2}{2} = \dfrac{4y + 20}{8y} $ This give us: $ \dfrac{4}{8y} = \dfrac{3}{8y} + \dfrac{4y + 20}{8y} $ If we multiply both sides of the equation by $8y$ , we get: $ 4 = 3 + 4y + 20$ $ 4 = 4y + 23$ $ -19 = 4y $ $ y = -\dfrac{19}{4}$